Interest rates are at $10\%$ for every maturity. Consider a bond with face value $$600,$ a coupon rate of $20\%$ and a maturity equal to $2$ years.

$1.$ Price the bond if the coupon is paid annually.

$2.$ Price the bond if the coupon is paid semiannually.

$3.$ Compare your answers in $(1)$ and $(2).$ Is there a difference and why?